Statistical properties of intermittent maps with unbounded derivative
Dynamical Systems
2008-12-16 v2
Abstract
We study the ergodic and statistical properties of a class of maps of the circle and of the interval of Lorenz type which present indifferent fixed points and points with unbounded derivative. These maps have been previously investigated in the physics literature. We prove in particular that correlations decay polynomially, and that suitable Limit Theorems (convergence to Stable Laws or Central Limit Theorem) hold for H\"older continuous observables. We moreover show that the return and hitting times are in the limit exponentially distributed.
Cite
@article{arxiv.0812.0555,
title = {Statistical properties of intermittent maps with unbounded derivative},
author = {Giampaolo Cristadoro and Nicolai Haydn and Philippe Marie and Sandro Vaienti},
journal= {arXiv preprint arXiv:0812.0555},
year = {2008}
}
Comments
23 pages, 2 figures